Finite Group Databasebeta

← #27205971

Subgroups — #27205971

Order 13184.

414 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 414 conjugacy classes of subgroups — too many to draw. Only its 113 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20268301C211yesmaximal, characteristic
2C2×#15692997C211yesmaximal, characteristic, complemented
3#20268131C212yesmaximal, complemented
4#20268127C211yesmaximal, characteristic, complemented
5#20268107C211yesmaximal, characteristic, complemented
6#20268048C212yesmaximal, complemented
7#20268034C212yesmaximal, complemented
8#20267950C212yesmaximal, complemented
9#20267947C211yesmaximal, characteristic, complemented
10#20267753C211yesmaximal, characteristic, complemented
11#448×C103C211yesmaximal, characteristic, complemented
12C2×#13110104C2211yescharacteristic
13C22×C4×D103C2211yescharacteristic
14C2×#13110095C2212yescomplemented
15C2×#13110088C2212yes—
16#15693003—21no—
17#15693001C2211yescharacteristic
18#15693000C2211yescharacteristic
19#15692997—21no—
20#15692997—21no—
21#15692997C2212yes—
22#15692997C2212yes—
23#15692992C2211yescharacteristic
24#15692989—21no—
25D4×Dic103—21no—
26(C22⋊D103)⋊C4—21no—
27#15692979C2211yescharacteristic
28C2×C4⋊Dic103C2211yescharacteristic
29C2×Dic103⋊C4—21no—
30C2×(C2×D103)⋊C4—21no—
31#15692955C2212yescomplemented
32#15692952C2212yescomplemented
33#15692946C2212yescomplemented
34#15692945C2212yescomplemented
35#15692942C2212yescomplemented
36C22⋊(C103⋊C8)C2211yescharacteristic
37(C2×D103)⋊C8C2212yes—
38C22×Q8×C103C2211yescharacteristic
39C2×SD16×C103C2212yescomplemented
40#121×C103C2211yescharacteristic
41#103×C103C2212yescomplemented
42C22⋊C8×C103C2211yescharacteristic
43C23×D103D411yescharacteristic
44#13110104—42no—
45C2×Dic206C2311yescharacteristic
46C2×C22⋊D103—21no—
47C2×C22⋊D103—21no—
48C22×Dic103—21no—
49C22×Dic103—21no—
50C22×Dic103D411yescharacteristic
51C2×C4×D103—42no—
52C2×C4×D103D411yescharacteristic
53C2×C4×D103D411yescharacteristic
54C2×C4×D103C2311yescharacteristic
55C2×C4×D103C2311yescharacteristic
56#13110095—42no—
57#13110088—42no—
58C2×C103⋊C8C2312yes—
59C4⋊Dic103—21no—
60C4⋊Dic103—21no—
61C4⋊Dic103C2312yes—
62C4⋊Dic103C2311yescharacteristic
63Dic103⋊C4—21no—
64Dic103⋊C4—22no—
65Dic103⋊C4—22no—
66C22⋊Dic103—21no—
67C22⋊Dic103—21no—
68(C2×D103)⋊C4—22no—
69(C2×D103)⋊C4—22no—
70(C2×D103)⋊C4—21no—
71(C2×D103)⋊C4—21no—
72C4×Dic103—21no—
73C2×Q8×C103—21no—
74C2×Q8×C103—42no—
75C2×Q8×C103C2312yes—
76C2×D4×C103—21no—
77C2×D4×C103C2311yescharacteristic
78C22×C4×C103—21no—
79C22×C4×C103C2311yescharacteristic
80SD16×C103—42no—
81C2×C8×C103C2312yes—
82C4⋊C4×C103C2311yescharacteristic
83C22⋊C4×C103—21no—
84C23×C103—21no—
85C23×C103C2×D411yescharacteristic
86C22×D103—22no—
87C22×D103—41no—
88C22×D103—41no—
89C22×D103C2×D411yescharacteristic
90C22×D103C2×D411yescharacteristic
91Q8×C103—22no—
92Q8×C103—22no—
93Q8×C103—42no—
94D4×C103—22no—
95D4×C103—42no—
96C2×C4×C103—22no—
97C2×C4×C103—21no—
98C2×C4×C103—22no—
99C2×C4×C103—42no—
100C2×C4×C103C2×D411yescharacteristic
101C2×C4×C103C2411yescharacteristic
102C22⋊D103—42no—
103C22⋊D103—42no—
104C2×Dic103—21no—
105C2×Dic103—22no—
106C2×Dic103—21no—
107C2×Dic103—41no—
108C2×Dic103—42no—
109C2×Dic103—42no—
110C2×Dic103C2×D411yescharacteristic
111C2×Dic103C2×D411yescharacteristic
112C4×D103—22no—
113C4×D103—22no—
114C4×D103—41no—
115C4×D103—41no—
116Dic206—22no—
117C8×C103—22no—
118C103⋊C8—22no—
119C22×C103—21no—
120C22×C103—21no—
121C22×C103—41no—
122C22×C103—41no—
123C22×C103—41no—
124C22×C103#13712yes—
125C22×C103C22×D411yescharacteristic
126C2×D103—21no—
127C2×D103—21no—
128C2×D103—21no—
129C2×D103—21no—
130C2×D103—21no—
131C2×D103—21no—
132C2×D103—44no—
133C4×C103—21no—
134C4×C103—42no—
135C4×C103—41no—
136C4×C103H(5,𝔽2)12yes—
137Dic103—21no—
138Dic103—21no—
139Dic103—41no—
140Dic103—42no—
141Dic103—41no—
142C2×C103—22no—
143C2×C103—81no—
144C2×C103#53411yescharacteristic
145C2×C103C2×#13711yescharacteristic
146C2×C103#57511yescharacteristic
147D103—41no—
148D103—41no—
149#3196—1031nomaximal, Sylow
150C103#319611yescharacteristic, complemented, Sylow
151#525—1031no—
152C2×C22⋊Q8—1031no—
153#485—1032no—
154#484—1031no—
155#481—1031no—
156#470—1032no—
157#468—1032no—
158#452—1032no—
159#451—1031no—
160#448D10311yescharacteristic, complemented
161#407—1031no—
162C2×#41—1031no—
163C22×Q8C2×D10311yescharacteristic
164C23×C4—1031no—
165C2×Q16—1032no—
166C2×SD16C2×D10312yescomplemented
167C2×M16—1032no—
168#123—2061no—
169C22⋊Q8—1032no—
170C22⋊Q8—1032no—
171C22⋊Q8—1031no—
172C22⋊Q8—1031no—
173C22⋊Q8—2061no—
174C22⋊Q8—2061no—
175#121—1031no—
176#121C2×D10311yescharacteristic
177#120—2061no—
178C4×D4—2061no—
179C4×D4—2061no—
180#117—1031no—
181C2×C4⋊C4—1031no—
182C2×C4⋊C4—2061no—
183C2×C22⋊C4—2061no—
184#107—1032no—
185#106—1032no—
186#103—1032no—
187#103—1032no—
188#103C2×D10312yescomplemented
189#102—1032no—
190C22⋊C8—1031no—
191C22⋊C8—1032no—
192C22⋊C8C2×D10311yescharacteristic
193C24—1031no—
194#41—4122no—
195C2×Q8—21no—
196C2×Q8—42no—
197C2×Q8—1031no—
198C2×Q8C22×D10312yes—
199C2×D4—21no—
200C2×D4—2061no—
201C2×D4—2061no—
202C2×D4C22×D10311yescharacteristic
203C22×C4—21no—
204C22×C4—1031no—
205C22×C4—1031no—
206C22×C4—1031no—
207C22×C4—1031no—
208C22×C4—1031no—
209C22×C4—4122no—
210C22×C4—2061no—
211C22×C4—2061no—
212C22×C4C22×D10311yescharacteristic
213Q16—4122no—
214SD16—42no—
215M16—4122no—
216C2×C8—1032no—
217C2×C8C22×D10312yes—
218C4⋊C4—1032no—
219C4⋊C4—1031no—
220C4⋊C4—2062no—
221C4⋊C4—2062no—
222C4⋊C4—2061no—
223C4⋊C4—2061no—
224C4⋊C4—2061no—
225C4⋊C4C22×D10311yescharacteristic
226C22⋊C4—21no—
227C22⋊C4—2062no—
228C22⋊C4—2062no—
229C22⋊C4—2061no—
230C22⋊C4—2061no—
231C22⋊C4—2061no—
232C22⋊C4—2061no—
233C42—2061no—
234C23—21no—
235C23—1031no—
236C23—1031no—
237C23—4121no—
238C23—4121no—
239C23—2062no—
240C23D4×D10311yescharacteristic
241Q8—22no—
242Q8—22no—
243Q8—42no—
244Q8—2062no—
245D4—22no—
246D4—42no—
247D4—4122no—
248D4—4122no—
249C2×C4—22no—
250C2×C4—21no—
251C2×C4—22no—
252C2×C4—42no—
253C2×C4—1031no—
254C2×C4—1031no—
255C2×C4—4121no—
256C2×C4—4121no—
257C2×C4—4122no—
258C2×C4—4122no—
259C2×C4—4121no—
260C2×C4—2061no—
261C2×C4—2062no—
262C2×C4—2061no—
263C2×C4—2062no—
264C2×C4—2062no—
265C2×C4D4×D10311yescharacteristic
266C2×C4C23×D10311yescharacteristic
267C8—22no—
268C8—2062no—
269C22—21no—
270C22—21no—
271C22—41no—
272C22—41no—
273C22—41no—
274C22—4124no—
275C22—2061no—
276C22—2061no—
277C22—2061no—
278C22—2061no—
279C22—2061no—
280C22—2061no—
281C22#1569305012yes—
282C22C2×D4×D10311yescharacteristic
283C4—21no—
284C4—41no—
285C4—42no—
286C4—4122no—
287C4—4121no—
288C4—4121no—
289C4—2061no—
290C4—2061no—
291C4#1569306612yes—
292C2—22no—
293C2—81no—
294C2—4121no—
295C2—4121no—
296C2#2026835111yescharacteristic
297C2C2×#1569305011yescharacteristic
298C2#2026859011yescharacteristic
subgroupG/H
centerC22C2×D4×D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#448×C103C2
socleC22×C103C22×D4
prime radical#20268301C2
hypercenter#448D103
hypocenterC103#3196
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C22×C4 ◁ #448

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×#15692997C2semidirect
3. #20268131C2semidirect
4. #20268127C2semidirect
5. #20268107C2semidirect
6. #20268048C2semidirect
7. #20268034C2semidirect
8. #20267950C2semidirect
9. #20267947C2semidirect
10. #20267753C2semidirect
11. #448×C103C2semidirect
14. C2×#13110095C22semidirect
31. #15692955C22semidirect
32. #15692952C22semidirect
33. #15692946C22semidirect
34. #15692945C22semidirect
35. #15692942C22semidirect
39. C2×SD16×C103C22semidirect
41. #103×C103C22semidirect
150. C103#3196semidirect
160. #448D103semidirect
166. C2×SD16C2×D103semidirect
188. #103C2×D103semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#202683012
C2×#156929972
#202681312
#202681272
#202681072
#202680482
#202680342
#202679502
#202679472
#202677532
#448×C1032
#3196103